Some choices are tough. Think of the last time you bought a car. You had to make a decision about price, color, gas mileage, electric or gas, size, horse power, and more. It’s possible one or two criteria were clear (i.e it had to be under $20,000 and red). Then you went shopping and found 5 red cars under $20k. But how do you factor in the other criteria?
To handle decision making with multiple criteria, Stuart Pugh (a product designer from Halifax, UK) developed the Pugh Matrix. It uses a simple arithmetic approach to decision-making.
What is a Pugh Matrix?
In short, a Pugh matrix (or decision-matrix) is a decision-making tool that quantifies the value of each option by ranking each choice on a set of criteria with values 1, 2, or 3, where the criteria can also carry a weight of importance to the decision. It is common in the SixSigma framework.
There are two types of Pugh Matrices:
- Weighted. Weighted Pugh matrices assign an order of importance to each criteria.
- Unweighted. Unweighted matrices consider all criteria of equal importance.
Let’s look more closely at his decision making invention below.
Example: Unweighted Pugh Matrix Template
It’s easy to make mistakes with the Pugh matrix because the “scoring” system is ternary (only 3 inputs values are allowed). Let’s take a look at a Pugh matrix template so you understand how to use it correctly.
Here is an unweighted Pugh matrix often used to evaluate delivery companies. There are 4 components to an unweighted Pugh matrix, and we can identify them all here:
- Criteria. the criteria in a Pugh matrix should be relatively qualitative. This is because, as a decision making tool, the goal is to help create meaning about how these options compare relative to each other, not to determine an absolute value.
- Options. Options are the possible choices you can make. The are the field heading for each column to the right of criteria.
- Values. There are only 3 possible values per option. They are -1 (below average), 0 (average), and 1 (above average), or 1, 2, 3. As stated above, the goal is to determine relative value, so no absolute numbers are needed here.
- Totals. Totals is exactly what is sounds like. It’s the score derived by adding up the -1, 0, or 1 mark under each category. We can see here that UPS is the clear winner, and that TNT is the clear loser.
Download the Excel Template to Follow Along
| Criteria | Option 1 – DHL | Option 2 – FedEx | Option 3 – USPS | Option 4 – UPS | Option 5 – TNT |
|---|---|---|---|---|---|
| Cost effectiveness | 1 | 0 | 1 | -1 | -1 |
| Timeliness | -1 | 0 | 1 | 1 | -1 |
| Quality assurance | 0 | 0 | 1 | 1 | -1 |
| Customer support | 0 | 0 | -1 | 1 | -1 |
| Global reach | 1 | 0 | -1 | 1 | 1 |
| Total | 1 | 0 | 1 | 3 | -3 |
Value of an Unweighted Pugh matrix
The value of an unweighted Pugh matrix is simplicity and clarity. It’s simple enough to execute on your own and with relatively little reflection (due to relative values). At the same time, writing down these relationships provides clarity.
But there’s something missing here. While all of these criteria are important, they’re not all equally important. Imagine you’re running a rubber-band company. Your product is not fragile. At the same time, it’s in high demand. This means that the quality assurance criteria is less important than the timeliness criteria. How can we account for this with a Pugh matrix?
Example: Weighted Pugh Matrix
We add another component to the 4 listed above: criteria weight. This component is what takes us from a unweighted Pugh matrix to a weighted one. Let’s take another look at our example above, but add in a column to the right of our criteria column.
If you downloaded the Excel sheet to follow along, you’ll see this matrix the Tab labelled “Weighted Pugh Matrix.”
| Criteria | Criteria Weight | Option 1 – DHL | Option 2 – FedEx | Option 3 – USPS | Option 4 – UPS | Option 5 – TNT |
|---|---|---|---|---|---|---|
| Cost effectiveness | 3 | 1 | 0 | 1 | -1 | -1 |
| Timeliness | 4 | -1 | 0 | 1 | 1 | -1 |
| Quality assurance | 1 | 0 | 0 | 1 | 1 | -1 |
| Customer support | 1 | 0 | 0 | -1 | 1 | -1 |
| Global reach | 1 | 1 | 0 | -1 | 1 | 1 |
| Total | 0 | 0 | 6 | 4 | -8 |
By adding a heavy weight to the timeliness criteria (4), the United States Postal Service takes the lead, and TNT’s expensiveness and timeliness problems become exacerbated.
In other words, a weighted Pugh matrix adds a level of relativity to the decision by adding importance to some criteria. Most professionals agree that a weighted matrix is superior to an unweighted one for this reason.
It’s important to note that the criteria weights must add up to 10. By using a 10-base system, we also show what percent weight each criteria holds. For example, Cost effectiveness has a weight of 30%, while Timeliness has a weight of 40%.
The way you should think about the calculation is shown in the Excel formula, but in simple terms, it’s multiplying each option’s criteria value by the criteria weight, then adding them together. For example, DHL would be (3*1)+(4*-1)+(1*0)+(1*0)+(1*1) = 0.
How to Build a Pugh Matrix
1. Define Options
The first step is to define your options. In our example of cars, these were Honda Civic, Fiat Panda, Nissan Lead, Ford Fiesta, and Toyota Corolla.
2. Define Decision Criteria
Now you need to decide what criteria you’ll use to evaluate those options. In the car example, these were price, color, gas mileage, small size, and horse power.
3. Define Weights for Decision Criteria (100%)
Next, assign a percent weight (totaling 100%) for each criteria. In the car example, these were:
- Price: 30%
- Color: 30%
- Gas Mileage: 10%
- Small Size: 20%
- Horse Power: 10%
4. Rank Options on Criteria Using Values -1, 0, 1 or 1, 2, 3
Now you need to “score” each option using a three-value system. In the car example, one example is the Honda Civic received these scores:
- Price: 3
- Color: 3
- Gas Mileage: 2
- Small Size: 1
- Horse Power: 3
5. Multiple Option Values by Criteria Weights
Next you need to multiple the option scores by the weight of the criteria. For the Honda Civic in our car example, this was:
- Price: 3*30% = 0.9
- Color: 3*30% = 0.9
- Gas Mileage: 2*10% = 0.2
- Small Size: 1*20% = 0.2
- Horse Power: 3*10% = 0.3
6. Add Results of all Criteria for Each Option
Finally, add the results of the weighted score per option to get its effective value. In the case of the Honda Civic, this is 0.9 + 0.9 + 0.2 + 0.2 + 0.3 = 2.5.
Best Practices
If you follow the above steps, you’re sure to have a quality result you can rely on. That said, here are some best practices to consider when building a Pugh Matrix:
- Always weight criteria. This will ensure you most accurately reflect the value of the options.
- Use weights that add to 100%. This will help you constrain the temptation to assign random values and eliminate an additional step to normalize the weights before applying them.
- Always assign weights before assigning values. This will ensure you “score” the criteria without any influence from the options.
- Collect as many options as you can. While not always possible, you should collect as many options as possible to provide the most representative sample possible.
Pugh Matrix for Supplier Selection
In a business context, especially when it come to business analysis, a common use case for the Pugh matrix is deciding on suppliers. If you think about it, a partnership is a big commitment.
In our personal lives, we have to think about some long term partnerships. For example, renting an apartment requires you think about multiple factors. Deciding on a cable plan, or which cloud storage service you will use both require evaluating a complex offer. These are all cases in which you could use a Pugh matrix, but because they’re low-risk decisions, we tend to go on feeling instead of carrying out a decision methodology.
However, in a business context, the stakes are much higher. Imagine you’re in a situation where you need to establish a relationship with a fabric provider. The problem is that you have four options, which are all slightly different. And the stakes are high. The contract you enter into must balance quality with cost effectiveness.
Pay too much, and you won’t be able to cover your fixed costs and pay salaries. Pay too little, and you’ll lose your credibility with clients. Then you have to think about responsiveness, customer support, duration of contract, and many other variables.
That’s why it’s important to have a weighted Pugh matrix when it comes to supplier selection. I encourage you to revisit the downloadable excel template. You can create your own supplier selection criteria, give them a weight rating that adds to 10, and see the results. Then you can compare what you see with what you thought.
Disadvantages
The Pugh Matrix has disadvantages. While it is a helpful decision-making tool, it cannot provide absolute truths about the value of the options. It’s limited to relative value in the eyes of the decision-maker. Moreover, the value assignments are subjective. If the creator of the matrix inputs a number with a bias, the output will have a bias as well. While the method limits uninformed decisions, it cannot wholly prevent them.
Pugh Matrix Pronunciation
You pronounce Pugh matrix as if there were only the first two letters, “Pu,” Make the “p” sound followed by a hard “u” letter noise. Another way to think of the pronunciation is by saying “P-you.” The “u” should sound like “you.” That’s how I would describe the pronunciation, but here’s an audio bit to hear it aloud:
Pugh Matrix in Six Sigma
We often hear about Pugh matrices in the context of Six Sigma, which is a development methodology used to eliminate defects in software and physical products. The reason you may hear about Pugh matrices and Six Sigma together is because the former brings a lot of value to the latter, though they are not inherently linked.
Six Sigma methodology preaches the use of a development built to weed out problems. The cycle steps are, in order, define, measure, analyze, improve, control. Pugh matrices are most important in the defining stage, though they often found their way into the control stage as well.
You can see why. When we’re defining what we want, we need to know what the options are and how much weight each criterion should have. What better way to do so than with a decision-matrix?
Other Names for Pugh matrix
This article is all about Pugh matrices, but the ideas herein are not exclusive to Stuart Pugh. In fact, the idea behind numeric decision-making matrices goes by multiple names. They each carry slight nuances, so don’t worry about knowing them by heart. You should just be aware in case others reference these titles.
Decision Matrix
As stated in the article title, decision matrices are just like Pugh matrices. They are specific to simple, or unweighted Pughs. They stand in contrast to the following: weighted matrices.
Weighted Matrix
When you hear “weighted matrix,” you should think weighted Pugh matrix. They are the same idea in principle. Some weighted matrices have additional weights. For example, you might weigh all criteria by one persepective, then weigh them additionally from another perspective.
The creates multi-level calculations that need to be standardized using a constant or multiplier. For example, let’s reuse our distribution provider example. USPS got a 1 for the criteria “cost effectiveness.” Using the weight, we multiply by 3, so the value after one weight is 3. However, perhaps we then weigh it by second standard, this time a fraction, say 20%. This is 0.6. We then compare to others to see where the weights stand, and reevaluate our response.
Options Matrix
Options matrix is an umbrella term that covers all kinds of matrices, including weighted pughs, unweighted pughs, double-weighted matrices, and more. While options matrix is the umbrella term, its also less common. The most important term to be familiar with is Pugh.
Conclusion
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